The following questions are accompanied by three statements A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question.
There are some red, blue and green balls in bag. What is the probability of getting a red ball if one ball is selected at random?
A. Ratio of number of green and blue balls in the bag is 4:3.
B. If we add 2 more red balls in the bag, the numbers of red balls will be equal to the number of green balls.
C. Sum of number of green and blue balls is twice the number of red balls in the bag.

Options

A. C alone
B. Either C alone or A and B together
C. Any two of the three together
D. Only A and B together

Answer

To determine the probability of selecting a red ball from a bag containing red, blue, and green balls, we need to find the number of red balls and the total number of balls in the bag. Let's analyze each statement provided to see if they give us the necessary information.

### Step-by-Step Solution:

1. **Understanding Probability**:
The probability of selecting a red ball is given by the formula:
\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} \]
To calculate this probability, we need to know both the number of red balls and the total number of balls in the bag.

2. **Analyzing Statement A**:
- **Statement A**: The ratio of the number of green and blue balls in the bag is 4:3.
- This statement gives us information about the relationship between green and blue balls but does not provide any information about the number of red balls. Hence, it does not help us find the probability of selecting a red ball.
- **Conclusion**: Statement A is **not sufficient**.

3. **Analyzing Statement B**:
- **Statement B**: If we add 2 more red balls in the bag, the number of red balls will be equal to the number of green balls.
- This statement indicates a relationship between red and green balls but does not provide the actual numbers of red balls or the total number of balls. We cannot determine the probability from this statement alone.
- **Conclusion**: Statement B is **not sufficient**.

4. **Analyzing Statement C**:
- **Statement C**: The sum of the number of green and blue balls is twice the number of red balls in the bag.
- This statement provides a relationship involving the total number of green and blue balls and the number of red balls. However, without knowing the actual counts of red balls or the total number of balls, we still cannot calculate the probability.
- **Conclusion**: Statement C is **not sufficient**.

5. **Combining Statements**:
- None of the statements A, B, or C alone provide enough information to determine the probability of selecting a red ball.
- Even when combined, they do not provide a clear picture of the actual counts of red balls or the total number of balls.

### Final Conclusion:
None of the statements A, B, or C are sufficient to answer the question regarding the probability of selecting a red ball from the bag.